【摘要】：類比推理能力在人類認(rèn)識(shí)世界和改造世界中起著啟發(fā)思想、拓寬思路、探索結(jié)論的作用�，F(xiàn)在,我國也開始逐漸關(guān)注對(duì)學(xué)生數(shù)學(xué)類比推理能力的培養(yǎng),但是單就碩博論文來看,我國對(duì)如何培養(yǎng)學(xué)生的數(shù)學(xué)類比推理能力的專項(xiàng)研究還不是很多,所提出的教學(xué)策略也不是很全面,教學(xué)步驟也不是很詳細(xì)。本文從理論和實(shí)踐兩個(gè)方面對(duì)如何在教學(xué)中培養(yǎng)學(xué)生的數(shù)學(xué)類比推理能力進(jìn)行了研究,得出了一些有價(jià)值的結(jié)論,可為一線數(shù)學(xué)教師提供參考。本文利用文獻(xiàn)查找法,總結(jié)了與本文有關(guān)的三個(gè)類比推理心理學(xué)研究理論,即結(jié)構(gòu)映射理論、實(shí)用圖式理論和認(rèn)知發(fā)展理論。利用問卷調(diào)查法,對(duì)盤山縣高級(jí)中學(xué)的部分學(xué)生及教師進(jìn)行了問卷調(diào)查,推理出我國高中生數(shù)學(xué)類比推理能力的現(xiàn)狀以及教師對(duì)培養(yǎng)學(xué)生數(shù)學(xué)類比推理能力的意識(shí)。本文以三大理論為指導(dǎo),結(jié)合調(diào)查結(jié)果,總結(jié)了培養(yǎng)高中生數(shù)學(xué)類比推理能力的教學(xué)策略和教學(xué)步驟。經(jīng)上述研究,本文得出一些結(jié)論:我國高中生的數(shù)學(xué)類比推理能力總體來說還比較低,其中由有限到無限的類比推理能力最低,由特殊到一般的類比推理能力好與其他類比推理能力。造成該現(xiàn)象的原因是,學(xué)生還沒有形成類比推理步驟。教師對(duì)培養(yǎng)學(xué)生的數(shù)學(xué)類比推理能力意識(shí)比較薄弱,是因?yàn)槲覈F(xiàn)在還沒有一套科學(xué)、明確、詳盡的培養(yǎng)高中生數(shù)學(xué)類比推理能力的教學(xué)步驟和相應(yīng)的教學(xué)素材。針對(duì)以上問題筆者認(rèn)為教師應(yīng)該利用數(shù)學(xué)知識(shí)結(jié)構(gòu)的相似性、性質(zhì)的相似性和研究方法的相似性以及類比問題所處情境和類比問題的呈現(xiàn)形式來培養(yǎng)學(xué)生的數(shù)學(xué)類比推理能力。教師在培養(yǎng)學(xué)生數(shù)學(xué)類比推理能力時(shí)應(yīng)該按照提出目標(biāo)問題、檢索源問題、類比對(duì)應(yīng)部分、得出類比結(jié)論、驗(yàn)證類比結(jié)論、習(xí)得類比結(jié)論這六步進(jìn)行。
[Abstract]:The ability of analogical reasoning plays an important role in understanding and transforming the world. Now, our country has begun to pay more and more attention to the cultivation of students' ability of analogical reasoning in mathematics. However, from the point of view of the thesis, there are not many special researches on how to cultivate students' ability of analogical reasoning in mathematics. The proposed teaching strategy is not very comprehensive, teaching steps are not very detailed. This paper studies how to cultivate students' ability of analogical reasoning in mathematics teaching from two aspects of theory and practice, and draws some valuable conclusions, which can be used as a reference for first-line mathematics teachers. In this paper, three theories of analogical reasoning psychology, namely, structural mapping theory, practical schema theory and cognitive development theory, are summarized by using the method of literature search. By using the method of questionnaire, some students and teachers of Panshan High School were surveyed, and the present situation of Chinese senior high school students' ability of mathematical analogical reasoning and their awareness of cultivating students' ability of mathematical analogical reasoning were inferred. Under the guidance of three major theories and combined with the results of the investigation, this paper summarizes the teaching strategies and teaching steps for cultivating the ability of mathematical analogy reasoning of senior high school students. Through the above research, this paper draws some conclusions: the ability of mathematical analogy reasoning of senior high school students in our country is still relatively low in general, among which the ability of analogy reasoning from limited to infinite is the lowest. The ability of analogy reasoning from special to general is good with other analogical reasoning ability. The reason for this phenomenon is that the students have not yet formed the analogical reasoning steps. Teachers' awareness of cultivating students' ability of analogical reasoning in mathematics is relatively weak, because there is not a set of scientific, clear and detailed teaching steps and corresponding teaching materials for cultivating students' ability of analogical reasoning in mathematics in our country. In view of the above problems, the author holds that teachers should use the similarity of mathematical knowledge structure, the similarity of nature, the similarity of research methods, the situation of analogical problems and the presentation of analogical problems to cultivate students' ability of mathematical analogical reasoning. When developing students' ability of analogical reasoning in mathematics, teachers should follow the six steps of raising objective problem, searching source problem, analogy corresponding part, drawing analogy conclusion, verifying analogy conclusion, and acquiring analogy conclusion.
【學(xué)位授予單位】：遼寧師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

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本文編號(hào)：2345559